To choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet with 10 different kinds of ice cream and 6 kinds of toppings, you can use the concept of combinations. The total number of ways to choose is 1800.
Explanation:To determine the number of ways to choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet, we can use the concept of combinations. We have 10 different kinds of ice cream to choose from, and we want to choose 3 of them. The number of combinations can be calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of objects (10 ice cream flavors) and r is the number of objects to be chosen (3 ice cream flavors), and ! denotes factorial.
In this case, the number of combinations of ice cream flavors is:
C(10, 3) = 10! / (3!(10-3)!) = 120
Similarly, we have 6 different kinds of toppings to choose from, and we want to choose 2 of them. The number of combinations of toppings is:
C(6, 2) = 6! / (2!(6-2)!) = 15
Therefore, the total number of ways to choose 3 kinds of ice cream and 2 kinds of toppings is the product of the number of combinations of ice cream flavors and toppings:
Total number of ways = 120 * 15 = 1800
Please someone help me !!! Thank you !!
Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.
Find the surface area of the rectangular solid.
l=16 in, w=13 in, h=15in.
Surface area is in inches and to the 2nd power.
The sum of the square of a positive number and the square of 3 more than the number is 45. what is the number?
The positive integer is [tex]3[/tex]
Let the number be [tex]a[/tex]
square of [tex]a = a^{2}[/tex]
Square of [tex]3[/tex] more than [tex]a[/tex] = [tex](3+a)^{2}[/tex]
[tex](3 + a)^{2} = (3+a)(3+a) = 9 + 3a + 3a + a^{2} = a^{2} + 6a + 9[/tex]
[tex]a^{2} + a^{2} + 9a + 9 = 45[/tex]
[tex]2a^{2} + 6a + 9 = 45[/tex]
Subtract 9 from both sides :
[tex]2a^{2} + 6a = 45 - 9[/tex]
[tex]2a^{2} + 6a = 36[/tex]
Divide through by 2
[tex]a^{2} + 3a = 18\\a^{2} + 3a - 18 = 0[/tex]
Factorize :
[tex]a^{2} + 6a - 3a - 18 = 0\\a(a + 6) - 3(a + 6) = 0\\a + 6 = 0\\or\\a - 3 = 0[/tex]
[tex]a = 3 ;\\or\\a = - 6[/tex]
since, a is a positive integer, then [tex]a = 3[/tex]
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Help please got to finish khan academy I’m really confused
PLEASE HELP
Missi designed a stained glass window and made a scale drawing using centimeters as the unit of measurement. She originally planned for the length of the window to be 44 in. but decided to change it to 48 in. If the length of the window in her scale drawing is 4 cm, which statement about the change of scale is true?
A)One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
B)One cm represented 44 in. in the first scale, but now 1 cm represents 48 in. in the second scale.
C)One cm represented 1 in. in the first scale, but now 1 cm represents 1 in. in the second scale.
D)One cm represented 12 in. in the first scale, but now 1 cm represents 11 in. in the second scale.
Answer:
The correct answer is option A,
One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale
Step-by-step explanation:
The earlier planned length was [tex]44 in\\[/tex]
So the scale of the map was
[tex]\frac{44}{4} \\= 11\\1 cm = 11 in\\[/tex]
The second planned length was [tex]48 in\\[/tex]
So the second scale of the map was
[tex]\frac{48}{4} \\= 12\\1 cm = 12 in\\[/tex]
Thus, option A is correct.
Compare the domains of the logarithmic function f(x) and the square root function g(x).
Graph of f(x):
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/al2_9_20a_media02.gif
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/img_alg02u09c03q25d_02.gif
In two or more complete sentences, explain whether or not the domains of the two functions are the same.
3. what is a popular sunday activity for families in mexico city ? ( 1point )
A. vista the beach
b. visit the prado museum
c. stroll by the roman aqueduct
d. go to the chapultepec park
In winter, the price of apples suddenly went up by 0.75 per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88
Which postulate or theorem can be used to prove that △JKL is similar to △MKN?
A. SSS Similarity Theorem
B. ASA Similarity Theorem
C. AA Similarity Postulate
D. SAS Similarity Theorem
Answer:
The correct option is D.
Step-by-step explanation:
In triangle △JKL,
[tex]\frac{JK}{KL}=\frac{30}{50}=\frac{3}{5}[/tex]
In triangle △MKN,
[tex]\frac{MK}{KN}=\frac{15}{25}=\frac{3}{5}[/tex]
In triangle △JKL and △MKN
[tex]\frac{JK}{KL}=\frac{MK}{KN}[/tex]
[tex]\angle JKL=\angle MKN[/tex] (Vertically opposite angles)
Since two sides are proportional and an inclined angle is congruent, so by SAS theorem of similarity we get
[tex]\triangle JKL=\triangle MKN[/tex]
Therefore option D is correct.
What is the value of x? Enter your answer in the box. x = . Triangle G E H with segment E D such that D is on segment G H, between G and H. Angle G E D is congruent to angle D E H. E G equals 99.2 feet, G D equals 62 feet, D H equals left parenthesis x plus 2 right parenthesis feet, and E H equals 112 feet.
Answer:
The value of x is 68 ft.
Step-by-step explanation:
Given information: [tex]\angle GED\cong \angle DEH[/tex]
Bisector of an angle of a triangle theorem states that an angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.
In triangle FEH, ED is an angle bisector
[tex]\frac{EH}{EG}=\frac{DH}{GD}[/tex]
[tex]\frac{112}{99.2}\times 62=x+2[/tex]
[tex]70=x+2[/tex]
[tex]70-2=x[/tex]
[tex]68=x[/tex]
Therefore the value of x is 68 ft.
Factor completely. a2+3a−28 Enter your answer in the box.
In the United States, the mean average height of adult women is approximately 65.5 inches, with a standard deviation of 2.5 inches. If height is normally distributed,what percent of the women in this country are between 63 and 70.5 inches tall?
banananana help me i need you
Answer:
Banananana. How do you know that person?
Step-by-step explanation:
The lowest common denominator for the fractions 8/64 and 8/32 is ?
Final answer:
The lowest common denominator for the fractions 8/64 and 8/32 is 32. This is found by identifying 32 as the least common multiple of the denominators 64 and 32, allowing both fractions to be expressed with the same denominator.
Explanation:
Finding the Lowest Common Denominator
To find the lowest common denominator (LCD) for the fractions 8/64 and 8/32, you must identify the smallest number that both denominators can divide into without leaving a remainder. Both 64 and 32 can be divided by 32, so the LCD for these fractions is 32. It's important to understand that finding an LCD involves looking for the least common multiple (LCM) of the denominators. In this case, since 32 is a multiple of 64 (32x2=64), it serves as the LCM of 32 and 64, and consequently, the LCD of the fractions.
To further clarify, each fraction can be expressed with a denominator of 32. For 8/64, when we divide both the numerator and denominator by 8, we get 1/8. This fraction can then be converted to have a denominator of 32 through multiplication by 4 (1/8 * 4/4 = 4/32). Similarly, the fraction 8/32 is already expressed with the desired denominator.
By finding the LCD, it is easier to perform addition, subtraction, or comparison of fractions, as they will share the same denominator.
The lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
To find the lowest common denominator (LCD) for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \)[/tex], we need to determine the least common multiple (LCM) of the denominators 64 and 32.
Step 1: Find the prime factorization of each denominator:
[tex]- \( 64 = 2^6 \)[/tex]
[tex]- \( 32 = 2^5 \)[/tex]
Step 2: Determine the LCM by taking the highest power of each prime that appears in any factorization:
[tex]\[ \text{LCM} = 2^{\max(6, 5)} = 2^6 = 64 \][/tex]
Therefore, the LCD of the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( 64 \).[/tex]
Step 3: Verify that ( 64 ) is indeed the LCD:
[tex]- \( \frac{8}{64} = \frac{1}{8} \)[/tex]
[tex]- \( \frac{8}{32} = \frac{1}{4} \)[/tex]
Both fractions can be rewritten with a denominator of ( 64 ):
[tex]- \( \frac{1}{8} = \frac{8}{64} \)[/tex]
[tex]- \( \frac{1}{4} = \frac{16}{64} \)[/tex]
Therefore, ( 64 ) is the lowest common denominator for[tex]\( \frac{8}{64} \) and \( \frac{8}{32} \).[/tex]
Thus, the lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
What is the equation of the exponential graph shown?
Kala bought two types of cheese at a deli. She bought 0.50 pound of American cheese and 1.25 pounds of Swiss cheese. The bar diagram and equation below represent Kala’s purchase, where p represents the total number of pounds of cheese she bought.
What is the total number of pounds of cheese Kala bought?
0.75
1.20
1.30
1.75
Answer:
The total number of pounds of cheese Kala bought is 1.75 pounds
Step-by-step explanation:
Kala bought two types of cheese at a deli.
She bought 0.50 pound of American cheese and 1.25 pounds of Swiss cheese.
The total number of pounds of cheese Kala bought
= 0.50+1.25
= 1.75 pounds
Hence, the total number of pounds of cheese Kala bought is:
1.75 pounds
The ratio of the amount of money Jason has to the amount of money Wilson has is 12:13. After Wilson spent $63, Jason had 3 times as much money as Wilson.
a. How much money did I Jason have?
b. How much money did they have altogether?
Factor completely 12a3d2 − 6ad3. Prime 6a3d3(2a − d) 6ad2(2ad − d) 6ad2(2a2 − d)
A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.
What is the perimeter of the resulting rectangle?
Enter your answer in the box.
PLS PLS PLS help I am rly confused
Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all? Enter your answer in the box. A pie chart depicting a count for bird species. Cardinals are at 13 percent, Sparrows are at 35 percent, Chickadees are at 23 percent, Blue Jays are at 8 percent, Woodpeckers are at 4 percent, and Robins are at 17 percent.Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all?
Answer: 120
Hope This Helps ^_^
Please help me! I don't know the answer.
Lines L and M are parallel. GEOMETRY
The angle measure of ∠2 is equal to 38°.
m∠2 = 38°.
What are the corresponding angles?When two parallel lines are crossed by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
Given:
Lines L and M are parallel lines.
And the parallel lines are cut by a traversal line.
From the property of corresponding angles:
The angle measure of ∠2 is equal to 38°.
Therefore, m∠2 = 38°.
To learn more about the corresponding angles;
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:)If Dani has 5,054 of a certain item and she needs to collect 6,000 of it, how much more does she need to reach her goal? :) Just for fun lol
5.11 find the probability of a couple having a baby girl when their third child is born, given that the first two children were both girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girls among three children?
Which measure describes how all of the values of a data set vary with a single number?
A) mean
B) median
C) mode
D) range
Answer:
The answer is d. range.
In oder to join a yoga club there is a $100 annual fee and a $5 fee for each class ytouattend. Write an equation in slope-intercept form that models this situation.
Matthew bought 4 new compact discs at $16.99 each and a carrying case for $35.89. He paid 2007-03-04-00-00_files/i0250000.jpg% sales tax on his purchases. If Matthew paid $112.42 total, determine if he paid the correct amount. a. Matthew paid $0.15 too little for his purchases. b. Matthew paid $0.16 too much for his purchases. c. Matthew paid $0.05 too much for his purchases. d. Matthew paid the correct amount for his purchases.
Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most $75000 and use at least 320 workers to build cars and motorbikes.
8000C+5500M≤75000 represents the number of cars C and motorbikes M the company can build by spending at most $75000.
52C+38M≥320 represents the number of cars and motorbikes the company can build by using at least 320 workers.
Can the company meet both of its expectations by building 4 cars and 6 motorbikes?
Which best describes the function on the graph?